IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 54, NO. 12, DECEMBER 2009 2745 A New Gaussian Mixture Algorithm for GMTI Tracking Under a Minimum Detectable Velocity Constraint John M. C. Clark, Panagiotis-Aristidis Kountouriotis, and Richard B. Vinter, Fellow, IEEE Abstract—This paper introduces a new methodology to account for Doppler blind zone constraints, arising, for example, in ground moving target indicator (GMTI) tracking applications. In such problems, target measurements are suppressed when the range rate (Doppler) of the target drops below a specified threshold in magnitude (the minimum detectable velocity). The proposed method, employing Gaussian mixture approximations to the fil- tering density, differs from earlier Gaussian mixture approaches in the way missed measurements are modelled. The distinctive feature of the algorithm, as compared with other Gaussian mix- ture filters, is that it is based on an exact calculation of the filtering density when a measurement is not recorded. Algorithms that result from applying this methodology are simple to implement and computationally undemanding. Simulation results indicate a uniform improvement in estimation accuracy over that of earlier proposed analytic techniques, and a tracking performance com- parable to that of state-of-the-art particle filters. Index Terms—Bayesian methods, blind Doppler, ground moving target indicator (GMTI) radar, minimum detectable velocity, target tracking. I. INTRODUCTION I N this paper we continue our study, early results of which were reported in [5] and [6], into a class of ground moving target indicator (GMTI) tracking problems. Here, the sensor provides noisy measurements of target range, bearing and range rate. A distinctive feature of GMTI trackers, as commonly im- plemented, is the introduction of a sensor data pre-processing stage, in which measurements are deliberately suppressed, whenever the magnitude of the range rate drops below a spec- ified threshold (the Minimum Detectable Velocity ). The purpose of artificially introducing the ‘Doppler blind zone’ (the region of the state space in which the range rate magnitude is small) is to separate out moving objects of interest from heavy, static clutter. For such a set-up, the occurrence, or non-occurrence, of a measurement in itself provides information about target motion. Manuscript received July 09, 2008; revised December 18, 2008, and March 31, 2009. First published November 03, 2009; current version published De- cember 09, 2009. Recommended by Associate Editor Z. Wang. The authors are with the Department of Electrical and Electronic Engi- neering, Imperial College, London, U.K. (e-mail: j.m.c.clark@imperial.ac.uk, pk201@imperial.ac.uk, r.vinter@imperial.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAC.2009.2031720 A key question in GMTI tracker design is how to exploit this information. In this paper we introduce a new Gaussian mixture filter for GMTI tracking that takes account of the Doppler blind zone in a particularly effective way, and give full details of the analysis underlying its construction. (We also allow for a non-unit proba- bility of detection, unrelated to the location of the measurement relative to the Doppler blind zone). The proposed filter, which we refer to as the noise related doppler blind mixture filter (NRDB), propagates a Gaussian mixture approximation of the conditional density of the state given measurements up to the present time. The algorithm is based on an exact calculation of the updated density, given a Gaussian mixture prior. The updated density, which is calcu- lated by conditioning on the events that the measured range rate lies in (or fails to lie in) the Doppler blind region, has the form of a weighted sum of densities that are easily calculated. The component densities are then approximated by Gaussian densi- tites with matched first and second moments. The NRDB filter is constructed according to the same philos- ophy—performing exact calculations of densities as far as pos- sible before introducing approximations—as the blind doppler mixture filter (BDMF) announced in [5] and elaborated (to take account of multiple models and the presence of clutter) in [6]. But the new filter differs from these predecessors, because it is based on a different model of the mechanism for suppressing measurements in the Doppler blind zone; according to the new model a measurement is returned, depending on whether the ob- served value of the noise-corrupted range rate is located in the Doppler blind zone, the latter being modeled as a binary region. 1 For the measurement model employed in the construction of the algorithm of [5], by contrast, the suppression of a measurement is based on the location of the exact range rate relative to the Doppler blind zone. We note that the new model is better matched to the practical data gathering process, since the decision to suppress a measure- ment is made on the basis of the noise-corrupted, not the exact, range rate observations. Surprisingly, even though the new filter is based on a more realistic noise process model, it is both sim- pler to implement and less computationally demanding than its predecessor [5]. Other filtering schemes based on matching first and second moments, preceeding [5] and [6], have been proposed for GMTI 1 There is either none, or there is a complete measurement attenuation, de- pending on the location of the noisy range rate relative to the Doppler blind zone. 0018-9286/$26.00 © 2009 IEEE Authorized licensed use limited to: Imperial College London. Downloaded on February 1, 2010 at 11:55 from IEEE Xplore. Restrictions apply. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Spiral - Imperial College Digital Repository